Novel Nonconforming Finite Element Methods for Maxwell's Equations

麦克斯韦方程组的新颖非协调有限元方法

基本信息

  • 批准号:
    0713835
  • 负责人:
  • 金额:
    $ 26万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2007
  • 资助国家:
    美国
  • 起止时间:
    2007-07-15 至 2011-06-30
  • 项目状态:
    已结题

项目摘要

The research in this project is based on the recent discovery of the PIs that numerical solutions of Maxwell's equations can be based on variational formulations that use function spaces where the divergence free condition is enforced. This is made possible by combining classical nonconforming finite elements for incompressible fluid flows and techniques from discontinuous Galerkin methods. In this new approach the boundary value problems of the time-harmonic (frequency-domain) Maxwell's equations are solved as elliptic problems, and the performance of the new nonconforming finite element methods for both the source (deterministic) problem and the eigenproblem (cavity resonance problem) is comparable to the performance of classical finite element methods for computational mechanics. In particular the discrete eigenvalues have neither spurious modes nor nonphysical zero eigenvalues. The proposed research will design and analyze many novel schemes for the Maxwell equations and the Maxwell eigenproblem using this new approach. Fast solvers (multigrid and domain decomposition methods) and adaptive algorithms will also be developed, with applications to related electromagnetic problems.The results of the proposed research will provide powerful computational tools for the design and analysis of electromagnetic devices such as antennas, radar sensors, waveguides, photonic crystals, magnetoresistive sensors and particle accelerators, with applications to diverse areas such as telecommunications, integrated optics, lasers, high energy physics, plasma physics, and nondestructive damage detection.
该项目的研究基于最近发现的 PI,即麦克斯韦方程组的数值解可以基于使用强制无散条件的函数空间的变分公式。 这是通过将不可压缩流体流动的经典非相容有限元与不连续伽辽金方法的技术相结合而实现的。在这种新方法中,时谐(频域)麦克斯韦方程的边值问题被求解为椭圆问题,并且新的非相容有限元方法对于源(确定性)问题和本征问题(腔共振问题)的性能与计算力学的经典有限元方法的性能相当。特别是,离散特征值既没有寄生模式,也没有非物理零特征值。拟议的研究将使用这种新方法设计和分析麦克斯韦方程组和麦克斯韦本征问题的许多新颖方案。还将开发快速求解器(多重网格和域分解方法)和自适应算法,应用于相关电磁问题。拟议研究的结果将为天线、雷达传感器、波导、光子晶体、磁阻传感器和粒子加速器等电磁设备的设计和分析提供强大的计算工具,并应用于电信、 集成光学、激光、高能物理、等离子体物理和无损损伤检测。

项目成果

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Susanne Brenner其他文献

Computer-assisted medical history taking prior to patient consultation in the outpatient care setting: a prospective pilot project
  • DOI:
    10.1186/s12913-024-12043-3
  • 发表时间:
    2024-12-18
  • 期刊:
  • 影响因子:
    3.000
  • 作者:
    Roman Hauber;Maximilian Schirm;Mirco Lukas;Clemens Reitelbach;Jonas Brenig;Margret Breunig;Susanne Brenner;Stefan Störk;Frank Puppe
  • 通讯作者:
    Frank Puppe
HEART FAILURE MEDICATION IN THE EXTENDED RANDOMIZED INH STUDY: CLINICAL OUTCOMES ACCORDING TO PRESCRIPTION FREQUENCY AND DOSING OF GUIDELINE-RECOMMENDED DRUGS
  • DOI:
    10.1016/s0735-1097(13)60764-0
  • 发表时间:
    2013-03-12
  • 期刊:
  • 影响因子:
  • 作者:
    Guelmisal Gueder;Stefan Stoerk;Goetz Gelbrich;Susanne Brenner;Caroline Morbach;Dominik Berliner;Ertl Georg;Christiane E. Angermann
  • 通讯作者:
    Christiane E. Angermann
OBSTRUCTIVE VENTILATORY DISORDER IN HEART FAILURE: NOT ALWAYS COPD!
  • DOI:
    10.1016/s0735-1097(10)61263-6
  • 发表时间:
    2010-03-09
  • 期刊:
  • 影响因子:
  • 作者:
    Susanne Brenner;Gülmisal Güder;Kilian Frö;hlich;Gö;tz Gelbrich;Roland Jahns;Berthold Jany;Georg Ertl;Christiane E. Angermann;Stefan Stö;rk
  • 通讯作者:
    Stefan Stö;rk
PREVALENCE AND PROGNOSTIC IMPACT OF ANEMIA AND RENAL INSUFFICIENCY: RELATION TO HEART FAILURE SEVERITY
  • DOI:
    10.1016/s0735-1097(11)60374-4
  • 发表时间:
    2011-04-05
  • 期刊:
  • 影响因子:
  • 作者:
    Gulmisal Guder;Goetz Gelbrich;Susanne Brenner;Burkert Pieske;Rolf Wachter;Frank Edelmann;Bernhard Maisch;Sabine Pankuweit;Georg Ertl;Stefan Störk;Christiane E. Angermann
  • 通讯作者:
    Christiane E. Angermann

Susanne Brenner的其他文献

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{{ truncateString('Susanne Brenner', 18)}}的其他基金

Finite Element Methods for Elliptic Least-Squares Problems with Inequality Constraints
具有不等式约束的椭圆最小二乘问题的有限元方法
  • 批准号:
    2208404
  • 财政年份:
    2022
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Novel Finite Element Methods for Elliptic Distributed Optimal Control Problems
椭圆分布最优控制问题的新颖有限元方法
  • 批准号:
    1913035
  • 财政年份:
    2019
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
US Participation at the Twenty-fifth International Domain Decomposition Conference
美国参加第二十五届国际域名分解会议
  • 批准号:
    1759877
  • 财政年份:
    2018
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Higher Order Variational Inequalities: Novel Finite Element Methods and Fast Solvers
高阶变分不等式:新颖的有限元方法和快速求解器
  • 批准号:
    1620273
  • 财政年份:
    2016
  • 资助金额:
    $ 26万
  • 项目类别:
    Continuing Grant
Finite Element Methods for Higher Order Variational Inequalities
高阶变分不等式的有限元方法
  • 批准号:
    1319172
  • 财政年份:
    2013
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Fast Interior Penalty Methods
快速内部惩罚方法
  • 批准号:
    1016332
  • 财政年份:
    2010
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid
多重网格理论与应用
  • 批准号:
    0738028
  • 财政年份:
    2007
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid
多重网格理论与应用
  • 批准号:
    0311790
  • 财政年份:
    2003
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid and Domain Decomposition Methods
多重网格和域分解方法的理论与应用
  • 批准号:
    0074246
  • 财政年份:
    2000
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant
Theory and Applications of Multigrid and Domain Decomposition Methods in Computational Mechanics
计算力学中多重网格和域分解方法的理论与应用
  • 批准号:
    9600133
  • 财政年份:
    1996
  • 资助金额:
    $ 26万
  • 项目类别:
    Standard Grant

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